基于分位数回归的华北落叶松干形曲线模拟

doi:10.13466/j.cnki.lyzygl.2020.01.019

林业资源管理 ›› 2020, Vol. 0 ›› Issue (1): 151-157.doi: 10.13466/j.cnki.lyzygl.2020.01.019

基于分位数回归的华北落叶松干形曲线模拟

付立华¹, 侯金潮¹, 孙赫², 王鹤智³, 刘强⁴, 程顺¹()

^1. 河北省塞罕坝机械林场,河北承德 068466
^2. 国家林业和草原局世界银行贷款项目管理中心,北京 100714
^3. 国家林业和草原局调查规划设计院,北京 100714
^4. 河北农业大学林学院,河北保定 071000

收稿日期:2019-11-25 修回日期:2019-12-16 出版日期:2020-02-28 发布日期:2020-05-18
通讯作者: 程顺 E-mail:chshaaaa@163.com
作者简介:付立华(1983-),女,河北承德人,硕士,主要从事森林经营管理等工作。Email: 342666087@qq.com
基金资助:
河北省林业科学技术研究项目(1708491)

Stem Shape Curves Simulation for Larixprincipis-rupprechtii Using Quantile Regressions

Lihua FU¹, Jinchao HOU¹, He SUN², Hezhi WANG³, Qiang LIU⁴, Shun CHENG¹()

^1. Saihanba Mechanized Forestry Farm of Hebei,Chengde,Hebei 068466
^2. World Bank Loan Project Management Center,National Forestry and Grassland Administration,Beijing 100714
^3. Academy of Forest and Grassland Inventory and Planning,National Forestry and Grassland Administration,Beijing 100714
^4. College of Forestry,Agricultural University of Hebei,Baoding,Hebei 071000

Received:2019-11-25 Revised:2019-12-16 Online:2020-02-28 Published:2020-05-18
Contact: Shun CHENG E-mail:chshaaaa@163.com

摘要/Abstract

摘要：

干形是反映树干外部形态的重要指标,也是评价干材价值的重要依据,而削度方程是描述树木干形好坏的一个重要定量指标,其对干形模拟的准确性直接决定着树干材积和森林蓄积的估算结果。以河北省塞罕坝机械林场华北落叶松人工林为研究对象,基于4个常见的简单削度方程,模拟了260株样木的干形曲线,采用调整后决定系数(R_a²)、均方根误差(RMSE)、平均误差(ME)和平均误差绝对值(MAE)评价模型的拟合效果和检验效果,筛选最优的基础模型,并利用分位数回归技术,构建人工华北落叶松干形曲线模型。结果表明,4个简单削度方程中,Kozak方程对华北落叶松干形的拟合效果最好(R_a²=0.934, RMSE=1.985cm),检验结果也是最优的(ME=0.125cm, MAE=1.212cm)。因此,基于Kozak方程,结合分位数回归技术建立了华北落叶松干形曲线,相较于基础模型,分位数回归模型的拟合优度进一步提高。当分位点设置为0.1时,模型对靠近下部和上部的树干干形拟合效果较好;当分位点设置为0.5时,模型对位于中部的树干干形拟合效果较好;当分位点设置为0.9时,模型对树干基部的拟合效果较好。可见,分位数回归技术使模型具有更强的灵活性。

关键词: 分位数回归, 干形曲线, 塞罕坝机械林场, 华北落叶松

Abstract:

Stem shape is an important index to reflect the external shape of stem and it is also an important basis for evaluating the value of trunk.The taper equation is an important quantitative index to describe the quality of tree stem shape.The accuracy of its simulation of stem shape directly determines the estimation of trunk volume and forest volume.In this study,four simple taper equations were used to estimate the stem shape of planted Larixprincipis-rupprechtii and the model fit and validation were assessed byadjusted determination coefficient(R_a²),root mean square error(RMSE),mean error(ME)and absolute mean error(MAE).The optimal model was selected and the taper shape of Larixprincipis-rupprechtii was modelled by using quantile regression technology.Result showed that Kozak equation has the best fitting result(R_a²=0.934, RMSE=1.985cm)and the validation result(ME=0.125cm, MAE=1.212cm)on the stem shape among the four simple taper equations.Thus,the taper shape of Larixprincipis-rupprechtii was established by using quantile regression technology based on Kozak equation.Compared with the basic model,the goodness-of-fit of quantile regression model was improved.When the quantile is set to 0.1,the model has a better fitting effect on the stem shape near the lower and upper part of trunk,when the quantile is set to 0.5,the model has a better fitting effect on the trunk at the middle part of trunk,and when the quantile is set to 0.9,the model has a better fitting effect on the base of trunk.It can be seen that quantile regression technology makes the model more flexible.

Key words: quantile regression, taper curve, Saihanba machinery forest farm, Larixprincipis-rupprechtii

中图分类号:

S758

付立华, 侯金潮, 孙赫, 王鹤智, 刘强, 程顺. 基于分位数回归的华北落叶松干形曲线模拟[J]. 林业资源管理, 2020, 0(1): 151-157.

Lihua FU, Jinchao HOU, He SUN, Hezhi WANG, Qiang LIU, Shun CHENG. Stem Shape Curves Simulation for Larixprincipis-rupprechtii Using Quantile Regressions[J]. FOREST RESOURCES WANAGEMENT, 2020, 0(1): 151-157.

图/表 7

表1

表2

基础模型形式

模型	表达式	来源
M1	d=a₁ $D a 2 H - h a 3 H a 4$	Demaerschalk^[19]
M2	d²/D²=b₁+b₂ $h / H$ +b₃ $h / H 2$	Kozak^[20]
M3	d/D= $1 - h / H c 1 1 / c 2$	Forslund^[21]
M4	d=D $e - d 1 h - 1.3$	Metcalf^[22]

表2

表3

参数估计结果及模型的拟合优度

模型	参数	估计值	置信区间95%		P 值	决定系数 ( $R a 2$ )	均方根误差 (RMSE/cm)
M1	a₁	1.7565(0.0921)	1.5677	1.9254	<0.001	0.888	5.080
	a₂	0.8658(0.0198)	0.8269	0.9045	<0.023
	a₃	0.7929(0.0077)	0.7778	0.0808	<0.001
	a₄	-0.7926(0.0242)	-0.8402	-0.7451	0.028
M2	b₁	1.5607(0.0125)	1.5362	1.5853	<0.001	0.934	1.985
	b₂	-3.2744(0.0663)	-3.4045	-3.1444	<0.001
	b₃	1.8807(0.0725)	1.7384	2.0229	<0.001
M3	c₁	1.3738(0.0216)	1.3313	1.4162	0.047	0.893	2.319
M3	c₂	1.3039(0.0201)	1.2645	1.3434	0.031	0.893	2.319
M4	d₁	0.0774(0.0009)	0.0754	0.0793	<0.001	0.905	2.417

表3

表4

模型的独立检验结果

模型	模型形式	平均误差(ME /cm)	平均误差绝对值(MAE/cm)
M1	d=1.7565D⁰^.⁸⁶⁵⁸ $H - h 0.7929$ H^-0^.⁷⁹²⁶	0.237	1.452
M2	d²/D²=1.5607-3.2744 $h / H$ +1.8807 $h / H 2$	0.125	1.212
M3	d/D= $1 - h / H 1.3738 1 / 1.3039$	-0.618	1.345
M4	d=D $e - 0.0774 h - 1.3$	-0.729	1.741

表4

表5

图1

图2

参考文献 30

[1]	Jiang Lichun, Brooks J R. Taper, Volume, and Weight Equations for Red Pine in West Virginia[J]. Northern Journal of Applied Forestry, 2008,25(3):151-153. doi: 10.1093/njaf/25.3.151
[2]	Yang Yuqing, Huang Shongming, Trincado G , et al. Nonlinear mixed-effects modeling of variable-exponent taper equations for lodgepole pine in Alberta,Canada[J]. European Journal of Forest Research, 2009,128(4):415-429. doi: 10.1007/s10342-009-0286-2
[3]	Kublin E, Breidenbach J, Kändler G . A flexible stem taper and volume prediction method based on mixed-effects B-spline regression[J]. European Journal of Forest Research, 2013,132(5-6):983-997. doi: 10.1007/s10342-013-0715-0
[4]	Kozak B, Munro D O, Smith J H G. Taper functions and their applicbtion in forest inventory[J]. The Forestry Chronicle, 1969,45(4):278-283. doi: 10.5558/tfc45278-4
[5]	孟宪宇 . 削度方程和出材表的研究[J]. 南京林产工业学院学报, 1982,5(1):122-133.
[6]	Max T B, Burkhart H E . Segmented polynomial regression applied to taper equations[J]. Forest Science, 1976,22:283-289.
[7]	CaoQuang V., Harold E. Burkhart,Timothy A.Max.Evaluation of Two Methods for Cubic-Volume Prediction of Loblolly Pine to Any Merchantable Limit[J]. Forest Science, 1980,26(1):71-80.
[8]	Newnham RM . Variable-form taper functions for four Alberta tree species[J]. Canadian Journal of Forest Research, 1992,22(2):210-223. doi: 10.1139/x92-028
[9]	Kozak A . A variable-exponent taper equation[J]. Canadian Journal of Forest Research, 1988,18(11):1363-1368. doi: 10.1139/x88-213
[10]	梅光义, 孙玉军 . 国内外削度方程研究进展[J]. 世界林业研究, 2015,28(4):44-49.
[11]	庞丽峰, 贾宏炎, 陆元昌等. 热带地区几个珍贵树种干形曲线研究[J]. 南京林业大学学报:自然科学版, 2016,40(5):93-98.
[12]	王明亮 . 理论造材: 削度方程和出材率表的编制[J]. 林业科学研究, 1998,11(3):271-276.
[13]	胡春祥, 杨胜利, 贾炜玮 . 落叶松人工林树干形状模型和可变参数[J]. 应用生态学报, 2011,22(7):1685-1701.
[14]	李元 . 红松人工林树干削度方程的研究[J]. 绿色科技, 2017,17:87-91.
[15]	欧建德, 吴志庄 . 峦大杉与杉木人工林的生长形质、林分分化和空间利用比较[J]. 东北林业大学学报, 2018,46(7):7-11.
[16]	姜立春, 马英莉, 李耀翔 . 大兴安岭不同区域兴安落叶松可变指数削度方程[J]. 2016,52(2):17-25.
[17]	陈振雄, 贺东北, 肖前辉 . 海南省桉树、木麻黄、马占相思削度方程研建[J]. 中南林业调查规划, 2012,3:11-14.
[18]	佟金权, 盛炜彤 . 杉木人工林广义干形模型的研究[J]. 林业科学研究, 2000,13(3):239-248.
[19]	Demaerschalk J P . Converting volume equations to compatible taper equations[J]. Forest Science. 1972,18:241-245. doi: 10.1093/forestscience/18.3.241
[20]	Kozak A.Munro D D, Smith JHG . Taper functions and their application in forest inventory[J]. The Forest Chronicle, 1969,45:278-283 doi: 10.5558/tfc45278-4
[21]	Forslund R R . The power function as a simple stem profile examination tool[J]. Canadian Journal of Forest Research, 1991,21(2):193-198. doi: 10.1139/x91-023
[22]	Metcalf C, Jessica E, Clark J S, Clark D A . Tree growth inference and prediction when the point of measurement changes:modelling around buttresses in tropical forests[J]. Journal of tropical ecology, 2008,25:1-12. doi: 10.1017/S0266467408005646
[23]	李凤日 . 测树学[M]. 北京: 中国林业出版社, 2019.
[24]	胥辉, 孟宪宇 . 天山云杉削度方程与材种出材率表的研究[J]. 北京林业大学学报, 1995,18(3):21-30.
[25]	Weiskittel A R, Hann D W, Kershaw J A, et al. Forest growth and yield modeling[J/OL].(2006 -09)[2019-10-10].https://www.researchgate.net/publication/228010008_Forest_Growth_and_Yield_Modeling .
[26]	Zang Hao, Lei Xiangdong, Zeng Weisheng . Height-diameter equations for larch plantations in northern and northeastern China:a comparison of the mixed-effects,quantile regression and generalized additive models[J]. Forestry, 2016,89(4):434-445. doi: 10.1093/forestry/cpw022
[27]	Ozçelik R, CaoQuang V., Trincado G, et al. Predicting tree height from tree diameter and dominant height using mixed-effects and quantile regression models for two species in Turkey[J]. Forest Ecology and Management, 2018,419:240-248.
[28]	Zhang Lianjun, Bi Huiquan, Gove JH , et al. A comparison of alternative methods for estimating the self-thinning boundary line[J]. Canadian Journal of Forest Research, 2005,35(6):1507-1514. doi: 10.1139/x05-070
[29]	Mehtätalo L, Gregoire TG, Burkhart HE . Comparing strategies for modeling tree diameter percentiles from remeasured plots[J]. Environmetrics, 2008,19(5):529-548. doi: 10.1002/env.v19:5
[30]	Bohora S B, CaoQuang V. Prediction of tree diameter growth using quantile regression and mixed-effects models[J]. Forest Ecology and Management, 2014,319:62-66. doi: 10.1016/j.foreco.2014.02.006

数据	统计量	树龄/a	数量/株	树高/m	胸径/cm
建模数据	最小值	41~43	195	8.95	7.76
	最大值			20.93	26.96
	平均值			14.94	17.98
	标准差			2.60	3.58
检验数据	最小值	41~43	65	9.28	9.61
	最大值			20.50	26.39
	平均值			15.01	17.80
	标准差			2.64	3.84

基于分位数回归的华北落叶松干形曲线模拟

Stem Shape Curves Simulation for Larixprincipis-rupprechtii Using Quantile Regressions

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 7

参考文献 30

相关文章 13

编辑推荐

Metrics

本文评价

分位点	参数	估计值	P 值	决定系数(R²)	均方根误差(RMSE/cm)
无	b₁	1.5572(0.0106)	<0.001	0.901	1.970
	b₂	-3.2725(0.0560)	<0.001
	b₃	1.8855(0.0615)	<0.001
τ=0.1	b₁	1.0717(0.0130)	<0.001	0.832	2.336
	b₂	-1.7107(0.0599)	<0.001
	b₃	0.6063(0.0538)	<0.001
τ=0.2	b₁	1.1344(0.0132)	<0.001	0.871	2.063
	b₂	-1.8030(0.0525)	<0.001
	b₃	0.6380(0.0446)	<0.001
τ=0.3	b₁	1.1959(0.0170)	<0.001	0.898	1.866
	b₂	-1.9254(0.0654)	<0.001
	b₃	0.7092(0.0541)	<0.001
τ=0.4	b₁	1.2745(0.0258)	<0.001	0.918	1.712
	b₂	-2.1056(0.0892)	<0.001
	b₃	0.8218(0.0698)	<0.001
τ=0.5	b₁	1.3887(0.0225)	<0.001	0.929	1.632
	b₂	-2.4285(0.0832)	<0.001
	b₃	1.0596(0.0709)	<0.001
τ=0.6	b₁	1.4966(0.0279)	<0.001	0.925	1.722
	b₂	-2.7285(0.0966)	<0.001
	b₃	1.2874(0.0812)	<0.001
τ=0.7	b₁	1.5870(0.0175)	<0.001	0.910	1.930
	b₂	-2.9328(0.0661)	<0.001
	b₃	1.4300(0.0654)	<0.001
τ=0.8	b₁	1.7031(0.0270)	<0.001	0.879	2.301
	b₂	-3.2287(0.0996)	<0.001
	b₃	1.6572(0.0951)	<0.001
τ=0.9	b₁	1.8189(0.0341)	<0.001	0.690	3.526
	b₂	-4.0681(0.1228)	<0.001
	b₃	2.7712(0.1265)	<0.001

[1]	许粲, 江腾达. 一种机载LIDAR数据估算森林蓄积参数的方法[J]. 林业资源管理, 2020, 0(3): 105-110.
[2]	林鑫, 庞勇, 李春干. 无人机密集匹配点云与机载激光雷达点云的差异分析[J]. 林业资源管理, 2020, 0(3): 58-62.
[3]	李志明. 基于分层的典型猴欢喜天然林特征分析[J]. 林业资源管理, 2020, 0(3): 72-77.
[4]	龚召松, 曾思齐, 贺东北, 龙时胜, 姜兴艳. 湖南楠木次生林断面积生长模型研究[J]. 林业资源管理, 2020, 0(2): 87-.
[5]	彭其龙, 陈哲夫, 陈端吕. 湖南栎类-马尾松天然混交林单木生长模型研究[J]. 林业资源管理, 2020, 0(2): 94-.
[6]	林丽丽, 郝振帮, 杨柳青, 高仰驰, 刘艳芬, 余坤勇, 刘　健. 林分郁闭度自动测量系统的研建与应用[J]. 林业资源管理, 2020, 0(2): 167-.
[7]	曾伟生, 曹迎春, 陈新云, 赵连清. 河北省主要树种单木和林分生长率模型研建[J]. 林业资源管理, 2020, 0(1): 30-37.
[8]	王露露, 刘雪强, 王丽霞, 马顺兴, 马瑞婷, 闫东锋. 内黄林场优势树种龄级结构优化调整及评价[J]. 林业资源管理, 2020, 0(1): 47-53.
[9]	金忠明, 曹姗姗, 王蕾, 孙伟. 天山云杉林无人机可见光影像树冠信息提取方法研究[J]. 林业资源管理, 2020, 0(1): 125-135.
[10]	曾伟生. 总体与林分水平的树高-胸径模型对蓄积量估计的影响分析[J]. 林业资源管理, 2019, 0(6): 38-41.
[11]	张江平, 丁贵杰. 贵州人工柳杉单株二元立木材积模型研究[J]. 林业资源管理, 2019, 0(6): 62-68.
[12]	吴宏炜, 田意, 黄光灿, 张伟志, 庄崇洋, 江希钿. 基于非线性度量误差的湿地松生长模型[J]. 林业资源管理, 2019, 0(6): 69-74.
[13]	王六如, 尹洪波. 新型便携式树木测高仪DZH-30在森林资源调查中的应用[J]. 林业资源管理, 2019, 0(6): 132-136.